Linear-scaling quantum calculations using non-orthogonal localized molecular orbitals

Burger, Steven K.; Yang, Weitao

doi:10.1088/0953-8984/20/29/294209

Cited by 19 publications

(46 citation statements)

References 37 publications

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“…10,27,39 The ground-state calculations not only demonstrate that NOLMOs are more compact/localized in space than OLMOs but also illustrate that accurate results can be achieved with smaller cutoff radii. Moreover, solution of the time-domain NOLMO-TDDFT equations, with low-scaling effort, was also investigated where NOLMO construction is repeatedly performed to maintain the sparsity of NOLMOs in a system.…”

Section: Introductionmentioning

confidence: 87%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Development of linear-scaling techniques, in particular for excited states, remains an active area of electronic structure theory. With sparse matrix techniques, linear-scaling calculations can be achieved by means of DAC-style fragment methods, localized molecular orbitals (LMOs), and density matrices.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Cui¹,

Fang²,

Yang³

2010

J. Phys. Chem. A

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Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method (J. Chem. Phys. 2004, 120, 9458 and J. Chem. Phys. 2000, 112, 4). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Cui¹,

Fang²,

Yang³

2010

J. Phys. Chem. A

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“…Various methods have been proposed to address this issue. One promising formulation is the direct minimization of energy . Such methods take advantage of physical localization of the solution, namely that the solution can be sought in terms of non‐orthogonal orbitals with local support.…”

Section: Introductionmentioning

confidence: 99%

Matrix‐Free Locally Adaptive Finite Element Solution of Density‐Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning

Davydov

Heister

Kronbichler

et al. 2018

Physica Status Solidi (b)

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In this paper, we propose a new numerical method to find the ground state energy of a given physical system within the Kohn–Sham density functional theory. The h‐adaptive finite element method is adopted for spatial discretization and implemented with matrix‐free operator evaluation. The ground state energy is found by performing unconstrained minimization with non‐orthogonal orbitals using the limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. A geometric multigrid preconditioner is applied to improve the convergence. The clear advantage of the proposed approach is demonstrated on selected examples by comparing the performance to other methods such as preconditioned steepest descent minimization. The proposed method provides a solid framework toward O(N) complexity for the locally adaptive real‐space solution of density functional theory with finite elements.

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“…For molecular systems, the NOLMOs have been demonstrated to be better localized than the corresponding OLMOs with a spatial spread reduced by 10-28%, 8 and this advantage has also been realized in the recent ground-state linear scaling calculations. 1 In this work, we reformulate the TDDFT in terms of nonorthogonal localized molecular orbitals. As NOLMO is the most localized representation of electronic degrees of freedom, it can be most efficient in computation and is particularly useful for linear scaling calculations.…”

Section: Introductionmentioning

confidence: 99%

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Cui

Fang

Yang

2010

Phys. Chem. Chem. Phys.

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Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio-and nano-systems.

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Linear-scaling quantum calculations using non-orthogonal localized molecular orbitals

Cited by 19 publications

References 37 publications

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Matrix‐Free Locally Adaptive Finite Element Solution of Density‐Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

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Linear-scaling quantum calculations using non-orthogonal localized molecular orbitals

Cited by 19 publications

References 37 publications

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems†

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems†

Matrix‐Free Locally Adaptive Finite Element Solution of Density‐Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Contact Info

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Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†